Method for forming domain-inverted structure and optical element with domain-inverted structure

ABSTRACT

A method for forming a domain-inverted structure includes the following: using a ferroelectric substrate ( 1 ) having a principal surface substantially perpendicular to the Z axis of crystals; providing a first electrode ( 3 ) on the principal surface of the ferroelectric substrate, the first electrode having a pattern of a plurality of electrode fingers ( 5 ) that are arranged periodically; providing a counter electrode ( 6 ) on the other side of the ferroelectric substrate so as to be opposite from the first electrode; and applying an electric field to the ferroelectric substrate with the first electrode and the counter electrode, thereby forming domain-inverted regions corresponding to the pattern of the first electrode in the ferroelectric substrate. Each of the electrode fingers of the first electrode is located so that a direction from a base to a tip ( 5   a ) of the electrode finger is aligned with the Y-axis direction of the crystals of the ferroelectric substrate. This method can provide a short-period uniform domain-inverted structure.

TECHNICAL FIELD

The present invention relates to a method for forming a domain-invertedstructure by applying an electric field, and an optical element that hasa domain-inverted structure and is applicable to an optical wavelengthconversion element, a polarizer, an optical switch, a phase modulator,or the like.

BACKGROUND ART

Domain inversion is a phenomenon in which the polarization of aferroelectric material is inverted forcibly. With the use of thisphenomenon, domain-inverted regions are arranged periodically inside theferroelectric material to form a domain-inverted structure. Thedomain-inverted structure is used, e.g., for an optical frequencymodulator that utilizes surface acoustic waves, an optical wavelengthconversion element that utilizes the domain inversion of nonlinearpolarization, or an optical polarizer that utilizes a domain-invertedstructure in the form of a prism or lens. In particular, an opticalwavelength conversion element with very high conversion efficiency canbe produced by periodically inverting the nonlinear polarization of anonlinear optical substance. When this optical wavelength conversionelement is used to convert the wavelength of light of a semiconductorlaser or the like, a small short-wavelength light source can be providedand applied to the field of printing, optical information processing, oroptical measurement and control.

The ferroelectric material has a displacement of charge of the crystalsdue to spontaneous polarization. The direction of the spontaneouspolarization can be changed by applying an electric field opposite tothe spontaneous polarization. The direction of the spontaneouspolarization varies depending on the type of crystal (material). Thecrystals of a substrate made of LiTaO₃, LiNbO₃, or a mixed crystal ofthem, i.e., LiTa_((1−x))Nb_(x)O₃ (0≦x≦1), have the spontaneouspolarization only in the C-axis direction. Therefore, the polarizationof these crystals is present in either of two directions (+ directionand − direction) along the C axis. The application of an electric fieldrotates the polarization by 180 degrees opposite to its originaldirection. This phenomenon is called domain inversion. The electricfield required for the domain inversion is called a polarizationelectric field. The polarization electric field is about 20 kV/mm atroom temperature for LiNbO₃ or LiTaO₃ crystals, and about 5 kV/mm forMgO:LiNbO₃.

When the ferroelectric material is transformed into crystals having asingle polarization direction, the process is referred to as “singledomain of polarization”. In general, the polarization is changed to asingle domain by applying an electric field at high temperatures aftercrystal growth.

As a conventional method for forming periodically domain-invertedregions, e.g., JP 4(1992)-19719 discloses that a comb-shaped electrodeis formed on a LiNbO₃(Lithium niobate) substrate and a pulse electricfield is applied to the comb-shaped electrode. In this method, thecomb-shaped electrode is formed on the + C plane of the LiNbO₃substrate, while a planar electrode is formed on the − C plane. The + Cplane is grounded, and a pulse voltage with a pulse width of 100 μs isapplied to the planar electrode on the − C plane so that thepolarization is inverted by the pulse electric field applied to thesubstrate. The electric field required to invert the polarization is notless than about 20 kV/mm. When the electric field of such a value isapplied to a thick substrate, the crystals of the substrate may bedamaged. However, a substrate having a thickness of about 200 μm canavoid the crystal damage caused by the applied electric field and alsocan form domain-inverted regions at room temperature. Thus, thedomain-inverted regions can be deep enough to penetrate the substrate.

A domain-inverted structure with a short period of 3 to 4 μm isnecessary to achieve a high-efficiency optical wavelength conversionelement. When an electric field is applied so as to form domain-invertedregions, the polarization directly under the electrode is inverted, andthen the domain-inverted regions expand in the lateral direction of thesubstrate. Therefore, it is difficult to provide a short-perioddomain-inverted structure. To solve this problem, a conventional methodemploys a pulse width of about 100 μs and applies a pulse voltage to theelectrode for a short time, thereby providing a short-perioddomain-inverted structure.

As a method for forming a short-period domain-inverted structure in aMg-doped LiNbO₃ substrate (referred to as MgLN in the following), e.g.,JP 6(1994)-242478 discloses a method for forming a periodicallydomain-inverted structure in a MgLN of a Z plate. In this method, acomb-shaped electrode is formed on the + Z plane of the MgLN, and thesubstrate is irradiated with corona from the underside, thus providing adomain-inverted structure that has a period of 4 μm and penetrates the0.5 mm thick substrate.

JP 9(1997)-218431 discloses a method for forming a domain-invertedstructure in an off-cut MgLN. An electrode is formed on the off-cut MgLNwhose polarization direction slightly tilts from the substrate surface,and a voltage is applied to the electrode, thus providing an aciculardomain-inverted structure. The domain-inverted regions grow in thepolarization direction of the crystals, and the domain-invertedstructure has a period of about 5 μm.

However, it has been difficult to form a fine domain-inverted structurein a Mg-doped LiTa_((1−x))Nb_(x)O₃ (0≦x≦1) substrate of a Z plate.Although the domain-inverted structure can be formed in the off-cutsubstrate by applying an electric field with the conventional method,only a complicated technique such as corona poling is known for forminga fine uniform domain-inverted structure in the Z-plate substrate. Inthe corona poling, charged particles are deposited on the substrate togenerate an electric field for inverting the polarization. However,there is a limit to the magnitude of the electric field generated by thecharged particles. Therefore, the thickness of a substrate available toform a domain-inverted structure is limited to about 0.5 mm, and thedomain-inverted structure cannot be formed in the substrate having alarge thickness of more than 1 mm. On the other hand, the application ofa voltage using the electrode is effective in forming a domain-invertedstructure in the off-cut substrate. However, such a system is not usefulto form a domain-inverted structure widely and uniformly in the Z plate.

JP 2001-66652 discloses that a comb-shaped electrode is formed on a MgLNof a Z plate, and a voltage is applied to the comb-shaped electrode,thereby providing a periodically domain-inverted structure. This methodhas the advantage of forming the periodically domain-inverted structureuniformly. However, the domain inversion is limited to part of the endof the electrode. Thus, it is difficult to form a domain-invertedstructure deeply and uniformly in a wide range of the substrate underthe electrode.

DISCLOSURE OF INVENTION

It is an object of the present invention to provide a method for forminga short-period wide domain-inverted structure deeply and uniformly in aferroelectric substrate.

A method for forming a domain-inverted structure of the presentinvention includes the following: using a ferroelectric substrate havinga principal surface substantially perpendicular to the Z axis ofcrystals; providing a first electrode on the principal surface of theferroelectric substrate, the first electrode having a pattern of aplurality of electrode fingers that are arranged periodically; providinga counter electrode on the other side of the ferroelectric substrate soas to be opposite from the first electrode; and applying an electricfield to the ferroelectric substrate with the first electrode and thecounter electrode, thereby forming domain-inverted regions correspondingto the pattern of the first electrode in the ferroelectric substrate. Inthis method, each of the electrode fingers of the first electrode islocated so that a direction from a base to a tip of the electrode fingeris aligned with the Y-axis direction of the crystals of theferroelectric substrate.

An optical element of the present invention includes a ferroelectricsubstrate having a plane substantially perpendicular to the Z axis ofcrystals, and a plurality of domain-inverted regions formed periodicallyin the ferroelectric substrate. Each of the domain-inverted regions hasa planar shape with axial symmetry, and the symmetry axes are parallelto each other. In this optical element, the domain-inverted regions areformed so that a direction of the symmetry axes is aligned with the Yaxis of the crystals of the ferroelectric substrate. The domain-invertedregions extend from the + Z plane to the − Z plane. The ratio of an areaof the domain-inverted regions penetrating from the upper to the lowersurface of the ferroelectric substrate with respect to a total area ofthe domain-inverted regions is 50% or less, or the mean depth of thedomain-inverted regions is 40% to 95% of the thickness of theferroelectric substrate.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is a plan view showing an electrode structure used in a methodfor forming a domain-inverted structure in Embodiment 1 of the presentinvention. FIG. 1B is a cross-sectional view of FIG. 1A.

FIG. 2A is a plan view showing the state of domain-inverted regionsformed by the method in Embodiment 1. FIG. 2B is a side view of FIG. 2A.

FIG. 3A is a perspective view for explaining the superiority of anelectrode having fine tips. FIG. 3B is a cross-sectional view of FIG.3A. FIG. 3C is a graph showing a change in characteristics of aferroelectric substrate with the expansion of domain-inverted regions.

FIGS. 4A and 4B are a plan view and a cross-sectional view showing a wayof expanding domain-inverted regions, respectively.

FIGS. 5A and 5B are a plan view and a cross-sectional view showing a wayof expanding domain-inverted regions, respectively.

FIG. 6 is a characteristic diagram showing the relationship between thelength Lr of domain-inverted regions formed by the method in Embodiment1 and the crystal orientation of a substrate.

FIG. 7A is a plan view showing another electrode structure. FIG. 7B is across-sectional view of FIG. 7A.

FIG. 8A is a plan view showing a method for forming a domain-invertedstructure of the present invention. FIG. 8B is a cross-sectional view ofFIG. 8A.

FIG. 9A is a plan view showing a method for forming a domain-invertedstructure of the present invention. FIG. 9B is a cross-sectional view ofFIG. 9A.

FIG. 10A shows an annealing temperature curve for explaining the causeand effect of the stability of domain-inverted regions. FIG. 10B showsthe relationship between the rate of temperature rise and the decrementof domain-inverted regions.

FIG. 11A is a plan view showing a method for forming a domain-invertedstructure in Embodiment 3. FIG. 11B is a cross-sectional view of FIG.11A.

FIG. 12 is a cross-sectional view showing the state of formation ofdomain-inverted regions in first and second electrodes in Embodiment 3.

FIG. 13 shows the relationship between the distance L between the firstand second electrodes and the length Lr of the domain-inverted regionsin Embodiment 3.

FIG. 14 shows the relationship between the temperature of an insulatingsolution and the length Lr of the domain-inverted regions in Embodiment3.

FIG. 15 shows the relationship between a substrate thickness and adomain-inverted period in Embodiment 3.

FIG. 16A is a plan view showing a method for forming a domain-invertedstructure in Embodiment 4. FIG. 16B is a cross-sectional view of FIG.16A.

FIG. 17 shows the relationship between the pulse width of an appliedvoltage and the length Lr of the domain-inverted regions in Embodiments3 and 4.

FIG. 18 is a perspective view showing an optical element in Embodiment6.

FIG. 19A is a plan view showing an optical deflector as an example ofthe optical element in Embodiment 6. FIG. 19B is a cross-sectional viewof FIG. 19A.

DESCRIPTION OF THE INVENTION

In the method for forming a domain-inverted structure of the presentinvention, the electrode fingers of the first electrode for applying anelectric field to the ferroelectric substrate are located so that adirection from the bases to the tips of the electrode fingers is alignedwith the Y-axis direction of the crystals of the ferroelectricsubstrate. Thus, fine domain-inverted regions can be formed. This effectis based on the fact that the expansion of domain inversion in theY-axis direction is several times larger and more uniform than that inthe X-axis direction. Moreover, a voltage is concentrated on each of thetips of the electrode fingers that are arranged periodically. Therefore,when domain inversion occurs in the Z-plate substrate by using the aboveelectrode, the domain-inverted regions can be formed efficiently.

In the method for forming a domain-inverted structure of the presentinvention, it is preferable that the electric field is applied to theferroelectric substrate so that the ratio of an area of thedomain-inverted regions penetrating from the upper to the lower surfaceof the ferroelectric substrate with respect to a total area of thedomain-inverted regions is suppressed to 50% or less. With thisconfiguration, a fine domain-inverted structure can be formed uniformly.In the ferroelectric substrate having a plane substantiallyperpendicular to the Z axis of the crystals, when the domain-invertedregions are formed partially and penetrate the substrate to cause ashort circuit between the electrodes, the expansion of thedomain-inverted regions is concentrated in those portions penetratingthe substrate and may interfere with uniform domain inversion.Therefore, suppressing such an area of the domain-inverted regions thatpenetrate the substrate is effective in ensuring the uniformity of adomain-inverted structure.

In this configuration, it is preferable that a thickness T of theferroelectric substrate is 1 mm or more.

It is preferable that the electric field is applied to the ferroelectricsubstrate so that a mean value of a depth D of the domain-invertedregions is 40% to 95% of the thickness of the ferroelectric substrate.This can provide the same effect as described above.

The above method is suitable particularly for the ferroelectricsubstrate of Mg-doped LiTa_((1−x))Nb_(x)O₃ (0≦x≦1).

The first electrode may be a comb-shaped electrode, and the electrodefingers may be in the form of stripes. Moreover, the electrode fingersof the first electrode may be in the form of triangles, and a vertex ofthe triangle may serve as the tip of each of the electrode fingers.Alternatively, each of the electrode fingers may have a shape that issymmetrical with respect to the axis along the direction from the baseto the tip of the electrode finger, and may be located so that the axisof symmetry is aligned with the Y-direction of the crystals of theferroelectric substrate.

It is preferable that a width of the tip of each of the electrodefingers is 5 μm or less.

It is preferable that the process of applying an electric field to theferroelectric substrate further includes applying a pulse voltage with afield intensity of E1 and applying a direct-current voltage with a fieldintensity of E2, and E1 and E2 satisfy E1>E2. With this configuration,the pulse shape of the applied voltage can be controlled so that uniformdomain-inverted regions are formed in the widest possible range of thesubstrate under the designed electrode while expanding along theelectrode. When domain inversion occurs in the Z-plate substrate byusing the electrode with tips, a voltage is concentrated on the tips,where the domain-inverted regions can be formed efficiently. Tofacilitate the expansion of the domain-inverted regions throughout theelectrode, it is useful to use the pulse voltage with the direct-currentvoltage as an applied electric field. In other words, domain nuclei arecreated by the pulse voltage, and domain-inverted regions can beexpanded from the domain nuclei by the direct-current voltage.

It is preferable that the field intensity E1 is larger than 6 kV/mm, andthe field intensity E2 is smaller than 5 kV/mm. Moreover, it ispreferable that the pulse voltage includes at least two pulse trains.

In the method for forming a domain-inverted structure of the presentinvention, it is preferable that the ferroelectric substrate isheat-treated at 200° C. or more after the domain-inverted regions areformed, and the generation of a pyroelectric charge in the ferroelectricsubstrate is suppressed during the heat treatment. This can improve thestability of the domain-inverted regions formed by the application of anelectric field, and also can reduce scattering due to domain inversion.

It is preferable that the upper and the lower surface of theferroelectric substrate are short-circuited electrically during the heattreatment. It is also preferable that a rate of temperature rise in theheat treatment is 10° C./min or less.

The above method is suitable for the ferroelectric substrate having apolarization electric field of 5 kV/mm or less. The crystals of theferroelectric substrate may have a substantially stoichiometriccomposition.

In the method for forming a domain-inverted structure of the presentinvention, it is preferable that a second electrode is provided on theprincipal surface and is located opposite to the first electrode with aspace between the tips of the electrode fingers of the first electrodeand the second electrode. The second electrode serves to assist theconcentration of an electric field on the tips of the first electrode.When the electric field is concentrated on the tips of the firstelectrode, domain nuclei are created, and thus domain inversion startsto grow quickly.

It is preferable that a shortest distance L between the tips of theelectrode fingers and the second electrode, and a thickness T of theferroelectric substrate satisfy L<T/2. With this configuration, theeffect of the second electrode can be obtained sufficiently. Therelationship between the distance L and the substrate thickness Taffects the electric field distribution of the tips of the electrodefingers. Therefore, if the distance L is T/2 or more, the effect of thesecond electrode becomes excessively small.

It is preferable that the domain-inverted regions are formed under thefirst electrode and the second electrode by applying a voltage betweenthe first electrode and the counter electrode. When a voltage is appliedindividually to the electrodes in the same plane, the domain-invertedregions are formed under each of the adjacent electrodes. Therefore,this configuration is very effective in forming the domain-invertedregions widely.

It is preferable that the above method further includes a first electricfield application process of applying a voltage between the firstelectrode and the counter electrode, and a second electric fieldapplication process of applying a voltage between the second electrodeand the counter electrode. It is also preferable that thedomain-inverted regions are formed under the first electrode and thesecond electrode by the first electric field application process and thesecond electric field application process. Moreover, it is preferablethat the first electric field application process and the secondelectric field application process are performed separately.

The second electrode may have a plurality of electrode fingers with tipsopposed to the tips of the electrode fingers of the first electrode, andthe electrode fingers of the second electrode may be located so that adirection from a base to a tip of the electrode finger is aligned withthe Y-axis direction of the crystals of the ferroelectric substrate.

It is preferable that a distance L between the first electrode and thesecond electrode is 50 μm≦L≦200 μm.

It is preferable that either of the first electric field applicationprocess and the second electric field application process applies anelectric charge at least 100 times larger than 2 PsA, where Ps isspontaneous polarization of the ferroelectric substrate and A is adesired area of the domain-inverted regions. It is also preferable thatthe first electric field application process applies a pulse voltagewith a field intensity of E1 and a pulse width of τ≦10 msec, the secondelectric field application process applies a direct-current voltage witha field intensity of E2 and a pulse width of τ≧1 sec, and E1 and E2satisfy E1>E2.

It is preferable that the electric field is applied to the ferroelectricsubstrate in an insulating solution at 100° C. or more. The angle θbetween the principal surface and the Z axis may be 80°≦θ≦100°. It isalso preferable that a thickness T of the ferroelectric substrate is 1mm or more, and a period Λ of the domain-inverted regions is 2 μm orless. Moreover, it is preferable that a depth D of the domain-invertedregions and the thickness T of the ferroelectric substrate satisfy D<T.

It is preferable that a thickness T of the ferroelectric substrate isT≧1 mm, an insulating layer is formed between the counter electrode andthe ferroelectric substrate, and a pulse voltage with a pulse width of 1msec to 50 msec is applied between the first electrode and the counterelectrode. The insulating layer may be a SiO₂ layer, a TO₂ layer or aTa₂O₅ layer. Alternatively, it is also preferable that a thickness T ofthe ferroelectric substrate is T≧1 mm, a semiconductor layer is formedbetween the counter electrode and the ferroelectric substrate, and apulse voltage with a pulse width of 1 msec to 50 msec is applied betweenthe first electrode and the counter electrode. The semiconductor layermay be a Si layer, a ZnSe layer, or a GaP layer.

In the optical element of the present invention, the ratio of an area ofthe domain-inverted regions penetrating from the upper to the lowersurface of the ferroelectric substrate with respect to a total area ofthe domain-inverted regions is 50% or less, or the mean depth of thedomain-inverted regions is 40% to 95% of the thickness of theferroelectric substrate. Thus, a fine domain-inverted structure can beformed uniformly. In the ferroelectric substrate having a planesubstantially perpendicular to the Z axis of the crystals, when thedomain-inverted regions penetrate the substrate to cause a short circuitbetween the electrodes, the expansion of the domain-inverted regions isconcentrated in those portions penetrating the substrate and mayinterfere with uniform domain inversion. Therefore, suppressing such anarea of the domain-inverted regions that penetrate the substrate iseffective in ensuring the uniformity of a domain-inverted structure.

The ferroelectric substrate may be Mg-doped LiTa_((1−x))Nb_(x)O₃(0≦x≦1). The domain-inverted regions may have a period of 4 μm or less.The ferroelectric substrate may have a thickness of 1 mm or more. It ispreferable that a thickness T of the ferroelectric substrate is 1 mm,and a period Λ of the domain-inverted regions is 2 μm or less. Moreover,it is preferable that a depth D of the domain-inverted regions and thethickness T of the ferroelectric substrate satisfy D<T. The angle θbetween the principal surface and the Z axis may be 80°≦θ≦100°.

Hereinafter, embodiments of the present invention will be described indetail with reference to the drawings.

EMBODIMENT 1

FIG. 1A is a plan view showing an electrode structure used in a methodfor forming a domain-inverted structure in Embodiment 1 of the presentinvention. FIG. 1B is a cross-sectional view of the electrode structure.

A first electrode 3 having a comb pattern is formed on a principalsurface 2 of an MgLN substrate 1. A plurality of electrode fingers 5constituting the first electrode 3 are arranged periodically in the formof narrow stripes. Therefore, fine tips 5 a of the electrode fingers 5are arranged periodically. A second electrode 4 is formed on theprincipal surface 2 and is located at a predetermined distance away fromthe tips 5 a of the first electrode 3. The first electrode 3 and thesecond electrode 4 are insulated electrically. A counter electrode 6 isprovided on the underside of the MgLN substrate 1 so as to be oppositefrom the first electrode 3 and the second electrode 4. The shape of thecounter electrode 6 may be, e.g., a rectangular plane that covers aregion corresponding to the first electrode 3 and the second electrode4, and no particular pattern is necessary.

The electrode fingers 5 of the first electrode 3 are located so that thesymmetry axis of each stripe is aligned with the Y-axis direction ofcrystals of the MgLN substrate 1. In other words, the tips 5 a extendfrom the bases of the electrode fingers 5 in the Y-axis direction.

A pulse generator 7 applies a controlled voltage to the MgLN substrate 1between the first electrode 3 and the counter electrode 6, so thatdomain-inverted regions are formed in a ferroelectric material betweenthe electrodes. The controlled voltage is a pulse voltage ordirect-current voltage having a predetermined voltage level or duration,which will be described in detail later.

To avoid the generation of electric discharge during the voltageapplication, the substrate 1 is placed in an insulating liquid or vacuum(10⁻⁶ Torr or less), and then a direct-current voltage is applied to thesubstrate 1. When domain inversion occurs, a current (referred to as“polarization current”) proportional to the magnitude of spontaneouspolarization of the ferroelectric material and the electrode area flowsbetween the first electrode 3 and the second electrode 4.

It has been difficult to form the domain-inverted regions in MgLN of a Zplate with high reproducibility, even if only a pulse, a direct-currentvoltage, or a voltage obtained by superimposing a pulse on adirect-current voltage is applied to the conventional electrodeconfiguration. In contrast, this embodiment can form a short-perioduniform domain-inverted structure by employing the following conditions.

The uniformity of a periodic structure in domain inversion means thestability of a period or duty ratio. When a domain-inverted structure isused for wavelength conversion, the uniformity affects the conversionefficiency. For example, when the domain-inverted structure is formedperiodically over a length of about 10 mm, the periodic structure isdisturbed in part. The main reason for such nonuniformity is that thedomain-inverted regions expand partially in the lateral direction, and aportion in which the duty ratio is disturbed significantly is presentlocally. In a conventional method, there were several tens of nonuniformportions per 10 mm of the domain-inverted structure. When the period was3 μm or less, the nonuniform portions covered almost all over the area.Therefore, the conversion efficiency was only about several to 50% of atheoretical value. In contrast, the improved uniformity of thisembodiment can be represented, e.g., by a few nonuniform portions orless per 10 mm of the domain-inverted structure. For wavelengthconversion, the improved uniformity results in very high conversionefficiency close to the theoretical value (90% or more).

The conditions of this embodiment mainly relate to

(a) electrode shape,

(b) relationship between an electrode direction and a crystal axis, and

(c) applied pulse shape.

When these factors satisfy specific requirements, a fine domain-invertedstructure can be formed uniformly.

First, (a) electrode shape is described below. Referring to FIGS. 2A and2B, the shape of domain-inverted regions that are formed in theferroelectric material when a voltage is applied by the first electrode3 having fine tips will be explained. Upon applying a voltage,domain-inverted regions 8 are formed in the end portion of the firstelectrode 3. At this time, an electric field is concentrated on the finetips 5 a of the electrode. Therefore, domain nuclei are created first inthis portion, and then the domain-inverted regions expand.

In an ideal domain-inverted structure, the domain-inverted regions havea small width W and a long length Lr. It becomes easier to control thedomain-inverted regions precisely as the width W is smaller. Forexample, if the width W is small, a short-period domain-invertedstructure can be formed. Moreover, the domain-inverted regions can bebroader as the length Lr is longer.

When the end of the pattern electrode is not fine but wide, thedomain-inverted regions cannot be formed uniformly. Since an electricfield is formed evenly under the electrode, the domain nuclei aregenerated everywhere, and the domain-inverted regions expand from thesenuclei. In contrast, the electrode structure of this embodiment allowsthe domain nuclei to be formed exactly at the end of the electrode.Therefore, the controllability of forming the domain-inverted regionscan be improved, resulting in a uniform domain-inverted structure. Thismethod is particularly useful for a substrate made of Mg-doped LiNbO₃,Mg-doped LiTaO₃, or a mixture of them, i.e., Mg-dopedLiTa_((1−x))Nb_(x)O₃ (0≦x≦1).

In particular, it is known that the domain-inverted regions formed inMg-doped LiTa_((1−x))Nb_(x)O₃ (0≦x ≦1) crystals have the rectificationproperties. Therefore, a current flows through the portions where thedomain-inverted regions are formed. Once the domain-inverted regions areformed, they expand from the inverted domains. In the portions where nodomain inversion occurs, the applied voltage is reduced due torectification of the domain-inverted regions, so that domain inversionis not likely to occur. Accordingly, the nonuniformity of thedomain-inverted regions is increased, which makes it difficult toprovide a uniform domain-inverted structure. This tendency is prominentparticularly for a fine shape.

The superiority of the electrode having fine tips is described below. Asshown in FIG. 3A, a comb-shaped electrode 11 is formed on the + Z planeof a MgLN substrate 10, and a planar electrode 12 is formed on the − Zplane of the MgLN substrate 10. When a voltage is applied between theelectrodes, an electric field 13 is concentrated on the end portion ofthe comb-shaped electrode 11. Therefore, the field intensity of the endportion is larger than that of the other portions. Consequently, domainnuclei are generated and act as a trigger for the expansion ofdomain-inverted regions 14 from the domain nuclei. In an electrodestructure with a flat end portion, however, the domain nuclei aregenerated at random positions due to the nonuniformity of crystals orthe presence of microdomain, and thus cannot be controlled easily. Onthe other hand, the electrode structure with a fine end portion of thisembodiment allows the electric field to be concentrated on the endportion of the electrode. The field intensity is increased locally inthe end portion, so that it is possible to control the positions atwhich the domain nuclei are to be generated. As shown in FIG. 3B, whenthe domain nuclei are generated in the end portion of the comb-shapedelectrode 11, the domain-inverted regions grow from these nuclei alongthe electrode to increase in length Lr. The use of the electrode havingfine tips can control the region in which the domain nuclei are to begenerated, and thus can provide a uniform domain-inverted structure.

In the case of electrode shape without fine tips, such as a ladderelectrode or planar electrode, the electric field is not concentrated inthe end portion, and domain nuclei are generated at random locationsunder the electrode. Therefore, the domain inversion cannot becontrolled, which makes it difficult to form a required uniform shape.Thus, the fine tips of the electrode fingers should have a width smallenough to draw the electric field applied by the electrode sufficiently.In this case, “to draw the electric field sufficiently” indicates thedegree of concentration of the electric field necessary for providing auniform domain-inverted structure. The tip width is preferably 5 μm orless, more preferably 2 μm or less because the domain-inverted structurecan have high uniformity, and further preferably 1 μm or less becausethe domain-inverted structure can be made finer.

As described above, the electric resistance of the domain-invertedregions is reduced significantly in MgLN. Therefore, the resistancedecreases when increasing the domain-inverted regions. While the amountof current of the applied pulse is maintained constant, the appliedvoltage decreases when increasing the domain-inverted regions, as shownin FIG. 3C. When the applied voltage is reduced to a polarizationvoltage Vc or less, the growth of the domain-inverted regions issuppressed automatically.

To increase the domain-inverted regions further, it is necessary toconsider a change in the electric characteristics of the domain-invertedregions. Referring to FIGS. 4A, 4B, 5A, and 5B, a polarization processof expanding the domain-inverted regions further is explained below. Asdescribed above, the growth of the domain-inverted regions 14 issuppressed with expansion. This may be avoided by setting a largecurrent value. However, under the initial conditions of a highresistance, a large current flows into the domain-inverted regions,causing a dielectric breakdown due to temperature rise or abrupt lateralexpansion of the domain-inverted regions. To prevent this, first, arelatively low current (e.g., at most 0.1 mA) flows to formdomain-inverted regions, as shown in FIGS. 4A and 4B. After the growthof domain inversion has been stopped, the maximum current value israised further to accelerate the growth of the domain-inverted regions,as shown in FIGS. 5A and 5B. By repeating these processes, the length Lrcan be made longer.

The second electrode 4 is effective in increasing the length Lr of thedomain-inverted regions. The second electrode 4 is located at a distanceL away from the tips of the first electrode 3. The second electrode 4serves to assist the concentration of the electric field on the tips 5 aof the first electrode 3. As described above, when the domain-invertedregions are formed, the electric field is concentrated on the tips ofthe first electrode 3 to create domain nuclei, and the domain inversionstarts to grow. The electric field distribution at the tips of the firstelectrode 3 is affected by the counter electrode 6 and the secondelectrode 4. The distance L between the first and second electrodes 3, 4and the substrate thickness T affect the electric field distribution atthe tips 5 a of the electrode fingers 5, and therefore significantlyaffect the length Lr of the domain-inverted regions to be formed.

The experiment showed that uniform domain inversion is likely to occurwhen the distance L is shorter than the substrate thickness T. If thedistance L is the substrate thickness T or more, the effect of thesecond electrode 4 may be too small to increase the length Lr. If thedistance L is excessively short, an electric discharge is generatedbetween the first and second electrodes 103, 104. Therefore, thedistance L is preferably 5 μm or more, and L<T/2 is more preferred toincrease the length Lr of the domain-inverted regions.

Next, (b) relationship between an electrode direction and a crystal axisis described below. The relationship between the direction of theelectrode fingers 5 and the length Lr of the domain-inverted regions wasevaluated. MgLN is a uniaxial crystal and has been considered as beingsymmetrical about a plane perpendicular to the Z axis. In particular,there would have been no dependence of the domain inversioncharacteristics on the X-axis and Y-axis directions. However, it becomesclear that the domain inversion characteristics of the Z-plate substratesignificantly depend on the X axis and Y axis of the crystals. FIG. 6shows the crystal axis dependence of the length Lr of thedomain-inverted regions to be formed. The direction of the electrodefingers 5 is rotated in the X-axis or Y-axis direction, and the lengthLr of the domain-inverted regions in each of the directions is expressedby a distance from the origin in FIG. 6. When the tips of the electrodefingers 5 are oriented in the Y-axis direction, and the axial directionof the electrode fingers 5 is aligned with the Y-axis direction, thelength Lr of the domain-inverted regions is very long. In contrast, whenthe electrode fingers 5 are arranged along the X-axis direction, thelength Lr is reduced by more than half.

The size of domain inversion varies more with the electrode fingers 5formed in the X-axis direction than with the electrode fingers 5 formedin the Y-axis direction. When the electrode fingers 5 are formed in theY-axis direction, a variation in size of the domain-inverted regions isseveral % or less, and the domain-inverted structure can be uniform andavailable for practical use. As long as the direction of the electrodefingers 5 tilts at ±10° or less with respect to the Y axis, the lengthLr is relatively long, and the domain-inverted structure can besufficiently uniform for practical use. If the direction of theelectrode fingers 5 tilts at ±5° or less, the uniformity can be improvedfurther. If the direction of the electrode fingers 5 tilts at more than±10°, the length Lr is reduced significantly while the nonuniformity isincreased.

As described above, the important conditions of forming a uniformdomain-inverted structure are that the electrode fingers having finetips are formed with the axial direction aligned with the Y-axisdirection of the crystals. In the process of formation of thedomain-inverted regions, an electric field is concentrated on the tipsof the electrode fingers, and the surface electric field of this portionis higher than that of the other portions, thereby creating domainnuclei. Subsequently, the domain-inverted regions expand under theelectrode fingers from the nuclei, so that domain inversion occurs. Inthis case, when the axial direction of the electrode fingers is orientedin the Y-axis direction, the domain inversion is likely to expand intheY-axis direction of the crystals, resulting in uniform domaininversion. If the electrode does not have fine tips, the domain nucleiare formed randomly, which leads to random expansion of thedomain-inverted regions. Thus, it is difficult to form a finedomain-inverted shape, particularly a uniform domain-inverted structureof 10 μm or less. When the tips of the electrode fingers are oriented inthe X-axis direction, it is difficult to form a fine structure uniformlywhile ensuring a sufficient length Lr.

As a pattern of the periodic shape of the first electrode, a triangularshape as shown in FIGS. 7A and 7B can be used in addition to the stripesof the comb-shaped electrode. A first electrode 3 a can form triangulardomain-inverted regions 9 periodically. The triangular periodicallydomain-inverted regions may be applied to a prism, a deflector, or thelike. For the triangular shape, the domain-inverted regions can be madelarger by arranging the symmetry axis along the Y-axis direction of thesubstrate crystals. In such a case, the vertex of a triangle serves as atip, and domain inversion occurs and grows from the vertex.

Next, the effect of (c) applied electric field waveform on domaininversion is described below. When a direct-current voltage was appliedbetween the electrodes to form fine domain-inverted regions of severalμm, the resultant domain-inverted regions were significantly nonuniform.Specifically, the domain nuclei were created in several portions of theelectrode, and the polarization was spread considerably from each of thenuclei and came into contact with the domain-inverted regions formed bythe adjacent electrode fingers. Thus, the domain-inverted regions werenot controlled precisely. When a pulse voltage having a pulse width of0.1 ms to 100 ms and an applied voltage of about 8 kV/mm was applied, afine domain-inverted structure was formed uniformly. A pulse electricfield with a pulse width τ≦10 msec was preferred as the applied electricfield. Moreover, it was possible to provide a uniform domain-invertedstructure by applying a plurality of pulse trains. When the appliedvoltage was 6 kV/mm or less, no domain-inverted region was formed.

Although the domain-inverted structure was provided by applying thepulse trains, the domain-inverted regions were formed only in thevicinity of the tips of the electrode fingers. Therefore, thedomain-inverted regions did not extend along the electrode fingers toincrease the length Lr. The result was the same when changing the pulseshape or pulse number. The optimum pulse number can be determined whileobserving the voltage waveform displayed by an oscilloscope. First, thevoltage amplitude at the beginning of the voltage application ismonitored, and additional pulses are applied. The voltage amplitudedecreases with increasing the number of pulses, and then is stopped whenthe applied pulses reach a certain number. There is a correlationbetween the saturation of the voltage amplitude and the minimum appliedpulse number. Accordingly, the applied pulse number can be determined bymonitoring the decrease of the voltage amplitude. Even if more pulsesthan the certain number are applied, the domain-inverted regions do notexpand. The minimum applied pulse number depends on the set current, andthe number decreases when increasing the current value. In other words,when a domain-inverted structure is formed with the same period, thegrowth of domain inversion is stopped by the application of a smallernumber of pulses as the current value becomes higher. Thus, even if morepulses than that number are applied, the domain-inverted regions do notexpand.

Then, a direct-current voltage was applied in addition to a pulsevoltage. The application time was about 1 to 100 sec. It was difficultto provide a uniform domain-inverted structure by applying only thedirect-current voltage. However, when the direct-current voltage wasapplied consecutively after the pulse trains, the domain-invertedregions expanded along the electrode, and the length Lr was severaltimes longer than the domain-inverted regions formed by applying onlythe pulses voltage. Thus, a fine uniform domain-inverted structure wasformed in a wide range of the substrate by applying the direct-currentvoltage after the pulse trains. The desired result was achieved underthe following conditions. The applied electric field pulse had, e.g., apulse width of 0.5 ms and a pulse number of about 200 to 5000. Theapplied voltage was 5 to 6 kV for the substrate having a thickness of 2mm. The maximum current value was about 0.2 to 1 mA. The direct-currentvoltage was considerably smaller than the pulse voltage, e.g., not morethan 0.2 to 4 kV/mm. Even with such a very low voltage, domain inversioncan occur. This is because the domain nuclei have been formed byapplying the pulse trains, and the application of the direct-currentvoltage may contribute to expansion of the domain-inverted regions fromthe domain nuclei. When a direct-current voltage of 5 kV or more wasapplied after the pulse application, the domain-inverted regions becametoo large to be fine.

Next, the need for limiting the maximum values of a current and avoltage practically during voltage application will be described. Asdescribed above, when the polarization of MgLN or the like is inverted,the electric resistance of the substrate is reduced significantly.Therefore, a large current flows into the domain-inverted regions. In ageneral ferroelectric material, the flow of charge is very small and isrestricted by the area of the domain-inverted regions. However, since acontinuous current flows through the MgLN, special consideration shouldbe given to a voltage circuit. Thus, it is necessary to have thefunction of controlling the maximum current flowing through the circuitto which an electric field is applied. For the MgLN, if the currentvalue is not controlled, a large current flows and may cause crystaldamage. To prevent this, a mechanism is required to reduce the appliedvoltage automatically so that the current value does not exceed thepredetermined maximum value. The maximum current for the actual MgLN maydepend on the electrode area, and preferably is 10 mA or less. In thecase of a short-period structure of 3 μm or less, the current valueshould be controlled to 5 mA or less.

In applying the pulse train, it is useful to apply a pulse voltage sothat the maximum current differs for each pulse. When a pulse electricfield is applied any number of times to produce domain inversion, thedomain-inverted regions have a high resistance in the early stages, andtherefore a high voltage can be applied with a small amount of current.The maximum current should be set as a low current of 1 mA or less atthe beginning of domain inversion, since increasing the amount ofcurrent may result in nonuniform domain-inverted regions. However, asthe domain-inverted regions expand, the resistance of thedomain-inverted regions decreases significantly. Therefore, if themaximum current value is limited, a voltage required for domaininversion cannot be obtained. Thus, it is useful to increase the maximumvalue of the applied current with expansion of the domain-invertedregions.

In the method for forming a domain-inverted structure of thisembodiment, the thickness of the MgLN substrate is preferably 1 mm ormore. When the thickness is 1 mm or more, the desired result can beachieved in both the uniformity of the domain-inverted structure and thelength Lr of the domain-inverted regions under the electrode. This isbecause a thick substrate can prevent the domain-inverted regions frompenetrating the substrate. As will be described later, if thedomain-inverted regions penetrate the substrate, the nonuniformity ofthe domain-inverted regions is increased, thus making it difficult toprovide a fine domain-inverted structure. By using the thick substrate,such penetration of the domain-inverted regions can be suppressed toprovide a uniform domain-inverted structure. Conventionally, theformation of the domain-inverted regions has been facilitated byreducing the substrate thickness to 0.5 mm or less, thus providing afiner domain-inverted structure. The phenomenon in which thedomain-inverted regions can be fine and uniform by increasing thesubstrate thickness is prominent particularly for a Mg-dopedLiTa_((1−x))Nb_(x)O₃ (0≦x≦1) substrate. The polarization voltage of theMg-doped LiTa_((1−x))Nb_(x)O₃ (0≦x≦1) substrate is not more thanone-fourth that of a general LN. When the substrate thickness isincreased, the general LN causes a dielectric breakdown due to thepolarization voltage. However, the Mg-doped LiTa_((1−x))Nb_(x)O₃ (0≦x≦1)substrate uses a lower polarization voltage, so that the polarizationvoltage can be applied without causing any dielectric breakdown.

The above method of this embodiment uses the Z-plate MgLN to form adomain-inverted structure. In the Z-plate substrate, the C axis of thecrystals is perpendicular to the substrate. Therefore, the electricfield application utilizing an electrooptic effect can be performedefficiently. Moreover, the Z-plate substrate has the advantage of, e.g.,increasing the depth of the domain-inverted regions, and is ideal for abulk-type optical element. However, the same effect also was observed inan off-cut substrate, which is close to the Z plate. As an off-cutangle, the angle between a line perpendicular to the substrate plane andthe C axis of the crystals was evaluated in the range of 0° or more.When the off-cut angle was not more than ±10°, a uniform domain-invertedstructure comparable to that of the Z plate was formed. When the off-cutangle was more than ±10°, it was difficult to provide a fine uniformdomain-inverted structure in the same manner.

In addition to MgLN with a congruent composition, the method for forminga domain-inverted structure of this embodiment also can be applied to aMg-doped LiTa_((1−x))Nb_(x)O₃ (0≦x≦1) substrate or a Mg-dopedLiTa_((1−x))Nb_(x)O₃ (0≦x≦1) substrate with a stoichiometriccomposition.

The doping amount of Mg and the domain inversion characteristics wereevaluated using the MgLN with a congruent composition. The substratethickness was 1 mm. The doping amount of Mg significantly affected thedomain inversion characteristics. A change in electric resistance due todomain inversion increased with the doping amount of Mg. The formationof a short-period domain-inverted structure also depended on the dopingamount of Mg. A short-period structure of 3 μm or less was formed onlyby the doping amount of Mg ranging from 4 to 5.5 μm. Along-periodstructure of 10 μm or more was formed even by the doping amount of Mgranging from 2 to 7 mol %. When the doping amount is more than 7 mol %,the crystallinity is degraded, and domain inversion is not likely tooccur. When the doping amount is less than 2 mol %, the lateralexpansion of domain inversion is increased, thus making it difficult toprovide a periodic structure. Therefore, the molar concentration ispreferably in the range of 2 to 7 mol % to form a periodic structure,and more preferably in the range of 4 to 5.5 mol % to form ashort-period structure.

For the composition of the substrate, the congruent composition wascompared with the stoichiometric composition, and there was not a largedifference in the relationship between the doping amount of Mg and thedomain inversion characteristics. The MgLN, MgLT, and Mg-dopedLiTa_((1−x))Nb_(x)O₃ (0≦x≦1) with a stoichiometric composition alsoindicated the same relationship between the doping amount of Mg and thedomain inversion characteristics.

It turned out that the depth of domain-inverted regions to be formedsignificantly affected the uniformity of the domain-inverted regions. Ina conventional method for forming a domain-inverted structure with aZ-plate MgLN substrate, the domain-inverted regions penetrate from theupper to the lower surface of the substrate. However, when ashort-period domain-inverted structure, particularly having a period of4 μm or less, is formed in the same manner, the nonuniformity isincreased significantly. The domain-inverted regions formed in the MgLNhave the rectification properties and allow a current to flow by theapplied voltage that is not more than a voltage at which domaininversion occurs. Therefore, when a voltage is applied between theelectrodes to produce domain inversion, part of the polarization isinverted and penetrates the substrate, and a current flows between theelectrodes through the domain-inverted regions. Consequently, while thepolarization grows largely in this portion, the growth of domaininversion is stopped in the other portions because the current has beenflowing into the portion where the polarization is inverted andpenetrates the substrate. Thus, the domain-inverted regions aresignificantly nonuniform.

In the case of domain inversion by direct-current application, it isdifficult to form fine domain-inverted regions. The reason for this isthe same as described above. The method for forming a domain-invertedstructure of this embodiment allows domain inversion to occur by pulseapplication, and thus can control a domain-inverted depth D not to reacha substrate thickness T. In other words, the applied pulse number can becontrolled so that the domain-inverted depth D does not reach thesubstrate thickness T, thereby limiting the proportion of penetration ofthe domain-inverted regions from the upper to the lower surface of thesubstrate. Thus, the uniformity of domain inversion can be improved. Theexperiment showed that the proportion of the area of the domain-invertedregions penetrating the substrate was suppressed to 1% to 50% of thetotal area of the domain-inverted regions, resulting in a uniformdomain-inverted structure. When the proportion was reduced to 20% orless, a fine structure of 4 μm or less was formed easily. By applying avery low direct-current voltage after the pulse voltage, thedomain-inverted regions expand from the domain nuclei formed by thepulse application along the electrode. Therefore, the domain-inverteddepth D is not increased and can be maintained smaller than thesubstrate thickness T. As described above, the relationship of T>D isestablished in forming the domain-inverted regions, which makes itpossible to provide a fine uniform domain-inverted structure.

To form fine domain-inverted regions uniformly by suppressing the growthof the domain-inverted regions penetrating the substrate, it is usefulto control the mean value of the domain-inverted depth D to be 40% to95% of the substrate thickness T. When the mean value is more than 95%,the proportion of penetration of the domain-inverted regions exceeds50%, and the nonuniformity of domain inversion is increasedsignificantly. When the mean value is less than 40%, there are manyportions where no domain-inverted region is formed, resulting in anonuniform domain-inverted structure. When the mean value is suppressedto 50% to 80% of the substrate thickness T, the uniformity can beimproved further.

For precise control of domain inversion, it is useful to change thecrystallinity of the surface of the MgLN substrate by ion exchange. Whenan electric field is applied to the MgLN by the pattern electrode, thesurface state of the substrate significantly affects the domaininversion characteristics. The application of a voltage using theelectrode allows the domain-inverted regions not only to grow directlyunder the electrode, but also to expand in the lateral direction. Thelaterally expanded domain-inverted regions are not likely to be fine.For example, when a periodically domain-inverted structure is formed,the lateral expansion of the domain-inverted regions makes it difficultto achieve a short-period structure. To prevent this, it is useful tosuppress the generation of domain nuclei. The domain nuclei are createdin the crystal surface directly under the electrode and in the vicinitythereof. The domain-inverted regions grow from these nuclei. Thegeneration of the domain nuclei can be reduced by performing ionexchange of the crystal surface to degrade the ferroelectricity of thecrystal. For example, when proton exchange (a kind of ion exchange) isperformed, the lateral expansion of the domain-inverted regions can besuppressed to provide a short-period domain-inverted structure. However,if the ion exchange depth is excessively deep, it becomes difficult toform the domain-inverted regions. Therefore, the ion exchange depth ispreferably 0.5 μm or less.

As shown in FIGS. 8A and 8B, the second electrode 4 may have comb-shapedelectrode fingers 15. This configuration can improve the yield offormation of the domain-inverted regions. When a voltage is appliedbetween the first electrode 3 and the counter electrode 6, an electricdischarge is generated between the first electrode 3 and the secondelectrode 4, and in some cases domain inversion does not occur. This hasbeen the cause of a lower yield of formation of the domain-invertedregions. The second electrode 4 having the comb-shaped electrode fingerssimilar to those of the first electrode 3 can prevent an electricdischarge between the electrodes, and also can improve the yield.

It turned out that domain inversion occurred in the lower portion of thefirst electrode 3 by applying a voltage between the second electrode 4and the counter electrode 6. When a distance between the secondelectrode 4 and the first electrode 3 is reduced, and a pulse voltage isapplied to the second electrode 4, domain-inverted regions are formed inthe lower portion of the first electrode 3. The domain-inverted regionsthus formed are uniform and do not penetrate the substrate. Thus, a finedomain-inverted structure can be formed uniformly. Moreover, theapplication of a voltage to each of the first electrode 3 and the secondelectrode 4 is repeated, so that the domain-inverted structure can bemade finer and longer.

As shown in FIGS. 9A and 9B, at least one of the first electrode 3 andthe second electrode 4 may be formed as a multilayer structure of ametal 16 and a dielectric 17. This configuration can improve theuniformity of domain inversion and expand the domain-inverted regionsformed under the electrode. The reason for this is that when a pulsevoltage is applied between the electrodes, the electrode capacitance isincreased to cause a change in transient properties of the pulse shape.The electrode in the form of a multilayer layer of metal and dielectricis effective in increasing the electrode capacitance. Preferred examplesof the dielectric include SiO₂, Ta₂O₅, Nb₂O₅, and other materials with ahigh dielectric constant.

EMBODIMENT 2

A method for forming a domain-inverted structure in Embodiment 2 isrelates to an improvement to stabilize domain inversion. First, theexperiment demonstrating the instability of domain inversion in MgLN isdescribed below.

In the experiment, a Mg-doped (5 mol) LiNbO₃ substrate of a Z plate wasused. An electrode was formed on the ±Z planes of the 1 mm thicksubstrate. A pulse voltage of about 10 kV was applied so as to formdomain-inverted regions under the electrode. The substrate was etchedwith a HF solution, and the domain-inverted regions were observed by adifference in etching rate of the ±Z planes.

Next, the substrate provided with the domain-inverted regions washeat-treated at about 100° C. for 30 minutes, followed by HF etchingtreatment. Thereafter, the domain-inverted regions were observed. Theobservation confirmed that the area of the domain-inverted regions wasreduced nearly by half. The observation also showed the following:

(1) the domain-inverted regions were reduced even by heat treatment at alow temperature of about 80° C.;

(2) the domain-inverted regions were reduced with temperature and timeof the heat treatment;

(3) the domain-inverted regions were reduced even by the application ofan electric field with a low voltage;

(4) a reduction in the domain-inverted regions occurred nonuniformly;and

(5) the same phenomena also were observed by using an off-cut substratein which the C axis of the crystals slightly tilts from a normal to thesubstrate surface.

As is evident from the above description, the domain-inverted structureformed by the electric filed application is significantly unstable inthe Z-plate MgLN. This may lead to the following problems.

The domain-inverted regions are reduced at a very low temperature.Therefore, the substrate provided with the domain-inverted regionscannot be processed by a process involving heating. Moreover, the domaininversion varies with time, and thus the element properties change withtime.

The method for forming a domain-inverted structure of this embodimentcan solve the above problems, and is characterized in that annealing isperformed after the domain-inverted regions have been formed by theapplication of an electric field, while the substrate and the electrodestructure may be the same as those in Embodiment 1. It is possible tosuppress a reduction in the domain-inverted regions by appropriatelysetting the conditions of annealing after the formation of thedomain-inverted regions.

The study on the appropriate annealing conditions showed that areduction in the domain-inverted regions significantly depends on therate of temperature rise of annealing. FIG. 10A shows an annealingtemperature profile. After the substrate reaches the annealingtemperature at a constant rate of temperature rise, annealing isperformed at 100° C. for 1 hour, and then the substrate is cooled toroom temperature at a constant rate of temperature fall. FIG. 10B showsthe result of measurement on the relationship between a rate oftemperature rise of annealing and a decrement of the domain-invertedregions. As can be seen from FIG. 10B, the decrement of thedomain-inverted regions increases with the rate of temperature rise.When the rate of temperature rise is more than 20° C./min, thedomain-inverted regions are reduced by 50% or more. In contrast, whenthe rate of temperature rise is 10° C./min or less, the decrement is 10%or less. When the rate of temperature rise is 5° C./min or less, thedecrement is several %. Therefore, the rate of temperature rise ispreferably 10° C./min or less, and more preferably 5° C./min or less tosuppress a reduction in the domain-inverted regions. The same experimentwas conducted on the rate of temperature fall and showed that the rateof temperature fall hardly affected a reduction in the domain-invertedregions. This is because an electric field due to a pyroelectric chargegenerated during the temperature rise may affect the stability of domaininversion.

It became clear that the instability of the domain-inverted regionsresulted from a reinversion phenomenon of the inverted domains caused bythe pyroelectric charge. Therefore, another method was studied to solvethis problem. For the Z-plate substrate, the pyroelectric charge appearson the upper and the lower surface of the substrate and produces anelectric field in the Z-axis direction. To prevent this, the upper andthe lower surface of the substrate may be short-circuited electrically.A metallic paste was applied to the upper and the lower surface of thesubstrate provided with the domain-inverted regions, and then the upperand the lower surface of the substrate were short-circuitedelectrically. Thereafter, the substrate was annealed. The annealingtemperatures were 400° C., 600° C., and 800° C. For the MgLN, althoughthe domain-inverted regions were reduced at 800° C., the stability ofdomain inversion was ensured even with any high-speed heat treatment at600° C. or less. Thus, when the upper and the lower surface of thesubstrate are short-circuited to eliminate the electric field due to thepyroelectric charge, high-speed annealing can be performed.

The annealing at 200° C. or more significantly improved the stability ofthe domain-inverted structure. After annealing was performed at 200° C.or more, the inverted shape was not changed at all by repeatinghigh-speed temperature rise and fall experiments at 100° C. or more.

Moreover, the scattering loss in the substrate was reduced significantlyby heat treatment at 400° C. or more, resulting in a domain-invertedstructure with high transparency. For example, when the domain-invertedstructure was applied to an optical wavelength conversion elementutilizing a nonlinear optical effect, the conversion efficiency wasincreased considerably. When the domain-inverted structure was appliedto a polarizer, the propagation loss was reduced by more than half.Therefore, it was possible to achieve a low-loss polarizer.

The instability of the domain-inverted structure is due to the fact thatthe polarization electric field of the MgLN is 5 kV/mm or less, which isone-fourth or less that of a general LiNbO₃, LiTaO₃, or the like.Because of a low polarization voltage, the inverted domains are notstable and susceptible to reinversion by a small pyroelectric effect.The polarization voltage also is low for the stoichiometric crystals,and thus heat treatment is required in the same manner. The upper limitof the heat treatment temperature depends on the Curie temperature ofthe substrate. The MgLN has a Curie temperature of about 1200° C.Therefore, the heat treatment temperature should be 800° C. or less.When it is more than 800° C., the domain-inverted regions are reduced.The Curie temperature of LiTaO₃ is about 600° C., and the upper limit ofthe heat treatment temperature is 500° C. or less.

The heat treatment of this embodiment is effective particularly for thedomain-inverted structure formed by the method of Embodiment 1. However,it also can be used to stabilize the domain-inverted structure formed byother methods.

EMBODIMENT 3

A method for forming a domain-inverted structure in Embodiment 3 ischaracterized by a voltage application process for the electrodestructure as shown in FIGS. 11A and 11B. In this embodiment, a MgLNsubstrate 1 has a principal surface 2 perpendicular to the Z axis. Afirst electrode 3 and a second electrode 4 are formed on the + Z planeof the MgLN substrate 1, and a voltage is applied using the firstelectrode 3 and the second electrode 4. In other words, when a voltageis applied to one of the electrodes, the domain-inverted regions alsoare formed under the other electrode. Thus, the domain-inverted regionscan be formed in a wide range of the substrate. An example of formingthe domain-inverted regions in the Z-plate MgLN substrate having athickness of 1 mm is described below.

In FIGS. 11A and 11B, the identical elements to those in Embodiment 1are denoted by the same reference numerals, and the explanation will notbe repeated. In this embodiment, a plurality of electrode fingers 5constituting the first electrode 3 are arranged at a predeterminedperiod so that the symmetry axis of each stripe is aligned with theY-axis direction of crystals of the MgLN substrate 1. Therefore, thetips 5 a extend from the bases of the electrode fingers 5 in the Y-axisdirection. The second electrode 4 also has the comb-shaped electrodefingers 15, and the tips 15 a extend from the bases of electrode fingers15 in the Y-axis direction.

A voltage controlled by the pulse generator 7 is applied between thefirst electrode 3 and the counter electrode 6 that is provided on theother side of the substrate, and thus domain-inverted regions are formedbetween the electrodes. If necessary, a pulse voltage or direct-currentvoltage having a predetermined voltage level can be applied to the MgLNsubstrate 1. To avoid the generation of electric discharge during thevoltage application, the MgLN substrate 1 is placed in an insulatingliquid or vacuum (10⁻⁶ Torr or less), and then a voltage is applied tothe substrate 1.

A voltage application process peculiar to this embodiment is describedbelow. First, a pulse voltage is applied between the second electrode 4and the counter electrode 6, followed by a direct-current voltage.Similarly, a pulse voltage is applied between the first electrode 3 andthe counter electrode 6, followed by a direct-current voltage. Thus,domain nuclei are generated under the tips 5 a of the first electrode 3and the tips 15 a of the second electrode 4, and domain inversionoccurs.

The reason that the application of a voltage to one of the first andsecond electrodes 3, 4 allows the domain inversion to occur under theother electrode is described below.

To examine the effect of the voltage applied to the second electrode 4on the portion under the first electrode 3, the state of domaininversion in the ferroelectric substrate was evaluated after a pulsevoltage was applied between the second electrode 4 and the counterelectrode 6, while no voltage was applied to the first electrode 3. Thedistance between the tips 5 a of the first electrode 3 and the tips 15 aof the second electrode 4 was 400 μm. After applying the voltage, thesubstrate was etched with a heated fluoronitric acid solution, anddomain inversion under the first electrode 3 was observed. Theobservation confirmed that the domain-inverted regions were formed underthe first electrode 3 to which no voltage had been applied. Similarly,when a voltage was applied to the first electrode 3, and no voltage wasapplied to the second electrode 4, the domain-inverted regions also wereformed under the second electrode 4.

This feature is described in more detail by referring to FIG. 12. FIG.12 is a cross-sectional view showing the state of formation of thedomain-inverted regions. When a voltage is applied to the secondelectrode 4, domain-inverted regions R2 are formed under the secondelectrode 4 and the first electrode 3. Subsequently, when a voltage isapplied to the first electrode 3, the domain-inverted regions under thefirst and second electrodes grow further and result in domain-invertedregions R1. This indicates that the domain-inverted regions can beexpanded by arranging two electrodes on the same plane and applying avoltage to either of the electrodes.

Next, the evaluation was conducted by changing the following conditionsso as to expand the domain-inverted regions formed under the firstelectrode 3.

(a) voltage application process

(b) distance between electrodes

(c) electrode direction and crystal axis

(d) voltage waveform and charge amount

(e) shape of the second electrode 4

(f) temperature of insulating solution

First, (a) voltage application process is described. As the voltageapplication process, simultaneous application (a voltage is applied tothe first and second electrodes 3, 4 simultaneously) and individualapplication (a voltage is applied to the first and second electrode 3, 4individually) were studied. In the simultaneous application, the amountof current flowing near the + Z plane was increased, and a large currentwas likely to flow into the same plane of the first electrode 3 and thesecond electrode 4, so that there was a very high possibility ofelectric discharge. Thus, the individual application is preferred forthe voltage application process. The individual application is describedbelow.

When an electric field is applied to the first and second electrodes 3,4 simultaneously, the electric field concentrated on the tips of each ofthe electrodes is reduced. This may interfere with the growth of thedomain-inverted regions. Therefore, it is effective to apply theelectric field individually in the early stages of the electric fieldapplication. Moreover, when the electric field is applied by one of theadjacent electrodes, domain inversion also occurs under the electrode towhich no voltage has been applied. Based on this action, the electricfield can be applied alternately by the adjacent electrodes, thusfurther expanding the domain-inverted regions formed under therespective electrodes. Moreover, the domain-inverted regions can be madelonger by the alternate application than by the application of anelectric field using a single electrode. In the experiment, e.g., whenthe distance between the electrodes was 200 μm, the length of thedomain-inverted regions formed by applying an electric field to a singleelectrode was about 2 times as long as that of the domain-invertedregions formed by applying a voltage to the first and second electrodes3, 4 simultaneously. With the alternate application, the length Lr ofthe domain-inverted regions was about 1.5 times longer than that of thesingle electrode application, and about 3 times longer than that of thesimultaneous application.

The application of an electric field alternately between the first andsecond electrodes was effective particularly in applying a pulseelectric field. Moreover, the domain-inverted regions formed under theelectrode to which an electric field is applied later tend to increasethe length Lr as compared with the electrode to which an electric fieldis applied before. Therefore, it is useful to apply an electric field tothe main electrode later.

When a direct-current electric field is applied after a pulse electricfield, there is no effect of the alternate application. The process canbe shortened by applying an electric field to the adjacent electrodessimultaneously. Moreover, the domain-inverted structure can be uniformas a whole. It is effective to apply the direct-current electric fieldto a plurality of electrodes simultaneously after the application of thepulse electric field.

Thus, as a preferred example, the electric field is applied by a firstelectric field application process of applying a voltage between thefirst electrode 3 and the counter electrode 6, and a second electricfield application process of applying a voltage between the secondelectrode 4 and the counter electrode 6. The first electric fieldapplication process applies a pulse voltage with a field intensity of E1and a pulse width of τ≦10 msec. The second electric field applicationprocess applies a direct-current voltage with a field intensity of E2and a pulse width of τ≧1 sec. E1 and E2 satisfy E1>E2.

Next, (b) distance between electrodes is described. FIG. 13 shows therelationship between the distance L between the tips 5 a of the firstelectrode 3 and the tips 15 a of the second electrode 4 and the lengthLr of the domain-inverted regions formed under the first electrode 3. Ascan be seen from FIG. 13, the length Lr increases when decreasing thedistance L between the first and second electrodes 3, 4. The length Lrstarts to be saturated when the distance L is close to 200 μm.Therefore, the distance L is preferably 200 μm or less. When thedistance L is too short (L≦50 μm), the possibility of electric dischargeis increased. In this embodiment, the desired result was achieved bysetting the distance L between the first and second electrodes 3, 4 toL=200 μm.

With respect to (c) electrode direction and crystal axis, theexplanation is the same as in Embodiment 1.

Next, (d) voltage waveform and charge amount will be described. Withrespect to the voltage waveform, the explanation is the same as inEmbodiment 1. The study on the amount of charge applied to the electrodeis as follows. The application of excess charge to the second electrode4 is effective in expanding the domain-inverted regions under the firstelectrode 3. For the second electrode 4, the appropriate charge amount Cis expressed by C=2Ps×A where Ps is spontaneous polarization and A is adomain-inverted area. By applying the amount of charge at least 100times larger than the appropriate charge amount C, the domain-invertedregions under the first electrode 3 is expanded, and the length Lr isincreased significantly. At this time, excessive charge is being appliedto the second electrode 4, and domain inversion occurs over the entiresurface under the second electrode 4. Thus, the periodic domaininversion in the form of a comb has been obliterated.

Next, (e) shape of the second electrode 4 is described. As an effectiveshape of the second electrode 4, the tips 15 a extend from the bases ofthe electrode fingers 15 in the Y-axis direction. However, the secondelectrode 4 is used as a dummy electrode for expanding thedomain-inverted regions under the first electrode 3. Therefore, thesecond electrode 4 may have other shapes as long as the domain-invertedregions under the first electrode 3 are expanded by the application ofan electric field. In fact, even if a rectangular electrode is used asthe second electrode 4, the domain-inverted regions under the firstelectrode 3 are expanded by the application of an electric field to thesecond electrode 4.

Next, (f) temperature of insulating solution will be described. Toprevent a dielectric breakdown during the application of an electricfield, it is preferable that the electric field is applied in theinsulating solution. FIG. 14 shows the relationship between thetemperature of the insulating solution and the length Lr of thedomain-inverted regions. As can be seen from FIG. 14, thedomain-inverted regions start to increase at near 80° C., and the lengthLr of the domain-inverted regions is saturated at 100° C. or more. Witha rise in temperature of the MgLN substrate, the polarization electricfield is decreased, and domain inversion may grow easily. When thetemperature is 150° C. or more, the growth of domain inversion in theperiodic direction becomes prominent. Thus, it is difficult to form auniform domain-inverted structure with a short period of 5 μm or less.Therefore, the temperature of the insulating solution is preferably 150°C. or less for short-period domain inversion. This condition also isapplied to the method of Embodiment 1.

According to the method for forming a domain-inverted structure in viewof the above conditions, a short-period (10 μm or less) uniformdomain-inverted structure was formed in the 1 mm thick Z-plate MgLNsubstrate with a large domain-inverted area. In the method of thisembodiment, the desired result was achieved when the thickness of theMgLN substrate was 1 mm or more. Specifically, the uniformity of thedomain-inverted regions and the length Lr of the domain-inverted regionsunder the electrode were improved with a substrate thickness of 1 mm ormore. This is because a thick substrate can prevent the domain-invertedregions from penetrating the substrate.

FIG. 15 shows the relationship between the substrate thickness T and thedomain-inverted period Λ at which domain inversion can occur. When thesubstrate thickness is 0.5 mm, it is very difficult to produce theperiodic domain inversion of 7 μm or less. By increasing the substratethickness, fine domain inversion can occur. As will be described later,when the domain-inverted regions penetrate the substrate, thenonuniformity of the domain-inverted regions is increased, thus makingit difficult to provide a uniform domain-inverted structure. The thicksubstrate can suppress penetration of the domain-inverted regions, sothat uniform domain-inverted regions can be formed. Conventionally, thesubstrate thickness has been reduced to 0.5 mm or less so as to formdomain-inverted regions, thus providing a finer domain-invertedstructure. The method for improving uniformity and fineness of thedomain-inverted regions easily by increasing the substrate thickness iseffective particularly for a Mg-doped LiTa_((1−x))Nb_(x)O₃ (0≦x≦1)substrate.

EMBODIMENT 4

A method for forming a domain-inverted structure in Embodiment 4 will bedescribed with reference to FIGS. 16A and 16B. The electrode structureof this embodiment is the same as that of Embodiment 3, except that aSiO₂ layer is sandwiched between the − Z plane of the MgLN substrate 1and the counter electrode 6 as an insulating layer 18. A low-frequencypulse voltage is applied between the electrodes, so that domain-invertedregions are formed widely under the electrode that is provided on the +Z plane.

As described in Embodiment 3, the MgLN has peculiar rectificationproperties. When part of the polarization is inverted and penetrates theMgLN substrate 1, a current flows into this portion, and thepolarization grows larger than in the other portions. Consequently, adesired voltage is not applied throughout the MgLN substrate 1, and thusthe growth of the domain-inverted regions is stopped, or the domaininversion becomes nonuniform. In particular, such nonuniformity isincreased significantly in forming a domain-inverted structure having aperiod of 4 μm or less.

To prevent the polarization from penetrating from the upper to the lowersurface of the MgLN substrate 1, and to improve the uniformity ofshort-period domain-inverted regions or to expand the domain-invertedregions, the SiO₂ layer is sandwiched between the − Z plane and thecounter electrode 6 and serves as the insulating layer 18 in thisembodiment. By sandwiching an insulator between the electrodes, it ispossible to increase the electrode capacitance, to improve theuniformity of domain inversion, and to expand the domain-invertedregions formed under the electrode. JP 7(1995)-281224 discloses astructure in which an insulator is sandwiched between electrodes. Thisdocument also discloses that the application time is set to 3 seconds sothat the domain-inverted regions having a period of 5 μm penetrate fromthe upper to the lower surface of the 0.3 mm thick substrate.

When a short-period domain-inverted structure is formed in the substratewith a thickness of 1 mm or more, it is very important to prevent thepenetration of polarization in the substrate. The penetration ofpolarization significantly depends on the pulse width of a pulse voltageto be applied. Therefore, the applied pulse shape was studied. First, apulse shape with a pulse width τ of 10 to 100 sec was applied. However,even if the current value was low, periodic domain inversion did notoccur, and an electric discharge or a phenomenon in which thepolarization was inverted over the entire surface was observed. This isattributed to a long applied pulse width. When applying a pulse shapewith the same pulse width (1 msec) as that has been used conventionally,the domain-inverted regions did not expand even by increasing the pulsenumber and the current.

After optimization of the pulse width, it was confirmed that thedomain-inverted regions expanded while the pulse width τ was in therange of 1 msec to 50 msec, as shown in FIG. 17. In particular, thedomain-inverted regions expanded significantly with a pulse width of 10msec to 50 msec. Moreover, when a domain-inverted width W was about 0.5Λ (Λ represents a domain-inverted period), the duty ratio was close to50%, and the highest efficiency was achieved. When the pulse width was 1sec or more, the domain inversion grew excessively in the widthdirection, resulting in W=Λ. The width of the domain-inverted regionswas larger than the period, and thus a domain-inverted structure was notprovided.

The expansion of the domain-inverted regions in using a 2 mm thick MgLNsubstrate was studied. The result also showed the dependence of thedomain inversion characteristics on the pulse width. That is, thedomain-inverted regions having a period of 4 μm expanded with a pulsewidth of 10 msec to 2 sec.

In this embodiment, a TiO₂ layer, a Ta₂O₅ layer, a Nb₂O₅ layer, or thelike can be used as the insulating layer in addition to the SiO₂ layer.

EMBODIMENT 5

In a method for forming a domain-inverted structure of Embodiment 5, aSi layer is used as a semiconductor layer, instead of a SiO₂ layer usedas the insulating layer 18 in the electrode structure of Embodiment 4.The Si layer (semiconductor layer) is sandwiched between the − Z planeand the counter electrode 6, thereby increasing the electrodecapacitance and preventing the polarization from penetrating thesubstrate. This can improve the uniformity of domain inversion andexpand the domain-inverted regions formed under the electrode.

Based on this embodiment using the semiconductor layer, the appliedpulse shape was studied. First, a pulse shape with a pulse width τ of 10to 100 sec was applied. However, even if the current value was low,periodic domain inversion did not occur, and an electric discharge or aphenomenon in which the polarization was inverted over the entiresurface was observed. This is attributed to a long applied pulse width.When applying a pulse shape with the same pulse width (1 msec) as thathas been used conventionally, the domain-inverted regions did not expandeven by increasing the pulse number and the current. After optimizationof the pulse width, it was confirmed that the domain-inverted regionsexpanded while the pulse width was in the range of 10 msec to 1 sec. Inparticular, the domain-inverted regions expanded significantly with apulse width of 20 msec to 50 msec.

The expansion of the domain-inverted regions in using a 2 mm thick MgLNsubstrate was studied. The result also showed the dependence of thedomain inversion characteristics on the pulse width. That is, thedomain-inverted regions having a period of 4 μm expanded with a pulsewidth of 10 msec to 2 sec.

In this embodiment, a ZnSe layer, a GaP layer, or the like can be usedas the semiconductor layer in addition to the Si layer.

EMBODIMENT 6

An optical element of Embodiment 6 can be produced by using the methodfor forming a domain-inverted structure of each of the aboveembodiments. A wavelength conversion element will be described withreference to FIG. 18 as an example of the optical element of thisembodiment. FIG. 18 is a perspective view of the wavelength conversionelement. Periodically domain-inverted regions 21 are formed in a Z-plateMgLN substrate 20. A fundamental having a wavelength λ can be convertedinto a harmonic having a wavelength λ/2 by wavelength conversion usingthe periodically domain-inverted structure. The domain-inverted periodis, e.g., 4 μm, and light with a wavelength of 900 nm can be convertedinto light with a wavelength of 450 nm. The thickness of the substrate20 is e.g., 1 mm and the depth of the domain-inverted regions 21 isabout 0.8 mm. The domain-inverted regions 21 extend along the Y axis ofcrystals of the substrate. The domain-inverted regions 21 also areformed from the + Z plane toward the − Z plane of the substrate 20. Mostof the domain-inverted regions 21 have a depth smaller than thethickness of the substrate 20. Although part of the domain-invertedregions 21 can penetrate the substrate 20, an area of thedomain-inverted regions 21 penetrating the substrate is not more than50% of a total area of the domain-inverted regions 21.

When the domain-inverted regions 21 were formed over a length of 10 mmin the X-axis direction, and light having a wavelength of 900 nm enteredthe substrate through a lens, the wavelength was converted with aconversion efficiency of 5%/W, and a 450 nm harmonic was obtained. Theresult showed that high-efficiency wavelength conversion was performedby forming uniform domain-inverted regions. When the thickness of thesubstrate 20 is 1 mm or more, the beam waist of the fundamental and theharmonic is increased. Thus, it is possible to reduce the power densityof light and to achieve a high output. The use of the 1 mm thicksubstrate can provide an output four times higher than that of a 0.5 mmthick substrate in which the domain-inverted regions are formed.

The domain-inverted regions 21 are formed in the Y-axis direction,thereby providing a short-period uniform domain-inverted structure. Thedomain-inverted structure may have a period of 2 μm or less, which makesit possible to generate ultraviolet light having a wavelength of 400 nmor less. Thus, short-wavelength light can be generated by forming thedomain-inverted regions 21 in the Y-axis direction. In contrast, whenthe domain-inverted regions 21 are formed in the X-axis direction, it isdifficult to provide a short-period domain-inverted structure, and onlylight having a wavelength of 500 nm or more is generated.

Moreover, the depth of the domain-inverted regions is smaller than thethickness of the substrate, and an area of the domain-inverted regionspenetrating the substrate is suppressed to 50% or less, therebyproviding a uniform domain-inverted structure. When the proportion ofthe domain-inverted regions penetrating the substrate is 1% to 50%, thedomain-inverted regions can be uniform. When the proportion is less than1%, the instability of the domain-inverted structure is increased, andthe domain-inverted regions vary with time. When the proportion is morethan 50%, it is difficult to provide a short-period domain-invertedstructure. Therefore, the wavelength conversion element thus producedcannot generate a second harmonic having a wavelength of 500 nm or less.By limiting the proportion of the domain-inverted regions penetratingthe substrate, uniform domain-inverted regions can be formed at adomain-inverted period of 3 μm or less, and ultraviolet light having awavelength of 400 nm or less can be generated.

In addition to the optical wavelength conversion element, the opticalelement utilizing the domain-inverted structure includes, e.g., apolarizer in which the domain-inverted structure is in the form of aprism or grating. The optical element also can be applied to a phaseshifter, a light modulator, a lens, or the like. Moreover, theapplication of a voltage to the domain-inverted regions can control achange in refractive index due to the electrooptic effect. Using thisfeature, the optical element can constitute, e.g., a switch, apolarizer, a modulator, a phase shifter, or beam shaper. The method ofeach of the above embodiments can provide a fine domain-invertedstructure, and thus can improve the performance of these opticalelements.

FIGS. 19A and 19B show an optical deflector that utilizes domaininversion in the form of a prism. Periodically prism-shapeddomain-inverted regions 23 are formed in a ferroelectric substrate 22.Electrodes 24, 25 are formed on the upper and the lower side of thedomain-inverted regions 23. The application of an electric field to theelectrodes 24, 25 causes a change in refractive index, and thus cancontrol the direction (e.g., an angle θ) of a beam 26. The electroopticeffect in which a refractive index changes with the electric fieldapplication depends on the polarization direction. Therefore, when theelectric field is applied as shown in the drawing, the sign of a changein refractive index is reversed between the domain-inverted regions 23and the non-inverted regions. Thus, it is possible to control thedirection of refraction of light in the prism portion.

In the above embodiments, the MgO-doped LiNbO₃ substrate is used as aferroelectric substrate. However, other substrates such as a MgO-dopedLiTaO₃ substrate, Nd-doped LiNbO₃ substrate, a KTP substrate, a KNbO₃substrate, a Nd and MgO-doped LiNbO₃ substrate, Nd and MgO-doped LiTaO₃substrate, and the same type of substrate having a stoichiometriccomposition also can be used. Among these substrates, the substratesincluding Nd-doped crystals can perform laser oscillation. Therefore,they can generate a fundamental by the laser oscillation at the sametime as a second harmonic by the wavelength conversion. Thus, it ispossible to provide a short-wavelength light source with high efficiencyand stable operating characteristics.

INDUSTRIAL APPLICABILITY

According to the present invention, a short-period wide domain-invertedstructure can be formed deeply and uniformly in a ferroelectricsubstrate, and an optical element with excellent properties such as anoptical wavelength conversion element can be produced.

1. A method for forming a domain-inverted structure comprising: using aferroelectric substrate having a principal surface substantiallyperpendicular to a Z axis of crystals of the ferroelectric substrate;providing a first electrode on the principal surface of theferroelectric substrate, the first electrode having a pattern of aplurality of electrode fingers that are arranged periodically; providinga counter electrode on the other side of the ferroelectric substrate soas to be opposite from the first electrode; and applying an electricfield to the ferroelectric substrate with the first electrode and thecounter electrode, thereby forming domain-inverted regions correspondingto the pattern of the first electrode in the ferroelectric substrate,wherein each of the electrode fingers of the first electrode is locatedso that a direction from a base to a tip of the electrode finger isaligned with a Y-axis direction of the crystals of the ferroelectricsubstrate, and the electric field is applied to the ferroelectricsubstrate so that a mean value of a depth D of the domain-invertedregions is 40% to 95% of the thickness of the ferroelectric substrate.2. The method according to claim 1, wherein the electric field isapplied to the ferroelectric substrate so that a ratio of an area of thedomain-inverted regions penetrating from the upper to the lower surfaceof the ferroelectric substrate with respect to a total area of thedomain-inverted regions is suppressed to 50% or less.
 3. The methodaccording to claim 2, wherein a thickness T of the ferroelectricsubstrate is 1 mm or more.
 4. The method according to claim 1, whereinthe ferroelectric substrate is Mg-doped LiTa_((1−x))Nb_(x)O₃ (0≦x≦1). 5.The method according to claim 1, wherein the first electrode is acomb-shaped electrode, and the electrode fingers are in the form ofstripes.
 6. The method according to claim 1, wherein the electrodefingers of the first electrode are in the form of triangles, and avertex of the triangle serves as the tip of each of the electrodefingers.
 7. The method according to claim 1, wherein each of theelectrode fingers has a shape that is symmetrical with respect to anaxis along the direction from the base to the tip of the electrodefinger, and is located so that the axis of symmetry is aligned with theY-direction of the crystals of the ferroelectric substrate.
 8. Themethod according to claim 1, wherein a width of the tip of each of theelectrode fingers is 5 μm or less.
 9. The method according to claim 1,wherein a process of applying an electric field to the ferroelectricsubstrate further comprises applying a pulse voltage with a fieldintensity of E1 and applying a direct-current voltage with a fieldintensity of E2, and E1 and E2 satisfy E1>E2.
 10. The method accordingto claim 9, wherein the field intensity E1 is larger than 6 kV/mm, andthe field intensity E2 is smaller than 5 kV/mm.
 11. The method accordingto claim 9, wherein the pulse voltage includes at least two pulsetrains.
 12. The method according to any claim 1, wherein theferroelectric substrate is heat-treated at 200° C. or more after thedomain-inverted regions are formed, and generation of a pyroelectriccharge in the ferroelectric substrate is suppressed during the heattreatment.
 13. The method according to claim 12, wherein the upper andthe lower surface of the ferroelectric substrate are short-circuitedelectrical during the heat treatment.
 14. The method according to claim12, wherein a rate of temperature rise in the heat treatment is 10°C./min or less.
 15. The method according to claim 1, wherein apolarization electric field of the ferroelectric substrate is 5 kV/mm orless.
 16. The method according to claim 1, wherein the crystals of theferroelectric substrate have a substantially stoichiometric composition.17. The method according to claim 1, wherein a second electrode isprovided on the principal surface and is located opposite to the firstelectrode with a space between the tips of the electrode fingers of thefirst electrode and the second electrode.
 18. The method according toclaim 17, wherein a shortest distance L between the tips of theelectrode fingers and the second electrode, and a thickness T of theferroelectric substrate satisfy L<T/2.
 19. The method according to claim17, wherein the domain-inverted regions are formed under the firstelectrode and the second electrode by applying a voltage between thefirst electrode and the counter electrode.
 20. The method according toclaim 19, further comprising: a first electric field application processof applying a voltage between the first electrode and the counterelectrode, and a second electric field application process of applying avoltage between the second electrode and the counter electrode.
 21. Themethod according to claim 20, wherein the domain-inverted regions areformed under the first electrode and the second electrode by the firstelectric field application process and the second electric fieldapplication process.
 22. The method according to claim 21, wherein thefirst electric field application process and the second electric fieldapplication process are performed separately.
 23. The method accordingto claim 17, wherein the second electrode has a plurality of electrodefingers with tips opposed to the tips of the electrode fingers of thefirst electrode, and the electrode fingers of the second electrode arelocated so that a direction from a base to a tip of each of theelectrode fingers is aligned with the Y-axis direction of the crystalsof the ferroelectric substrate.
 24. The method according to claim 17,wherein a distance L between the first electrode and the secondelectrode is 50 μm≦L≦200 μm.
 25. The method according to claim 20,wherein either of the first electric field application process and thesecond electric field application process applies an electric charge atleast 100 times larger than 2PsA, where Ps is spontaneous polarizationof the ferroelectric substrate and A is a desired area of thedomain-inverted regions.
 26. The method according to claim 20, whereinthe first electric field application process applies a pulse voltagewith a field intensity of E1 and a pulse width of τ≦10 msec, the secondelectric field application process applies a direct-current voltage witha field intensity of E2 and a pulse width of τ≧1 sec, and E1 and E2satisfy E1>E2.
 27. The method according to claim 1, wherein the electricfield is applied to the ferroelectric substrate in an insulatingsolution at 100° C. or more.
 28. The method according to claim 1,wherein an angle θ between the principal surface and the Z axis is80°≦θ≦100°.
 29. The method according to claim 1, wherein a thickness Tof the ferroelectric substrate is 1 mm or more, and a period Λ of thedomain-inverted regions is 2 μm or less.
 30. The method according toclaim 29, wherein a depth D of the domain-inverted regions and thethickness T of the ferroelectric substrate satisfy D<T.
 31. The methodaccording to claim 1, wherein a thickness T of the ferroelectricsubstrate is T≧1 mm, an insulating layer is formed between the counterelectrode and the ferroelectric substrate, and a pulse voltage with apulse width of 1 msec to 50 msec is applied between the first electrodeand the counter electrode.
 32. The method according to claim 31, whereinthe insulating layer is a SiO₂ layer, a TiO₂ layer or a Ta₂O₅ layer. 33.The method according to claim 1, wherein a thickness T of theferroelectric substrate is T≧1 mm, a semiconductor layer is formedbetween the counter electrode and the ferroelectric substrate, and apulse voltage with a pulse width of 1 msec to 50 msec is applied betweenthe first electrode and the counter electrode.
 34. The method accordingto claim 33, wherein the semiconductor layer is a Si layer, a ZnSelayer, or a GaP layer.
 35. An optical element comprising: aferroelectric substrate having a plane substantially perpendicular to aZ axis of crystals of the ferroelectric substrate; and a plurality ofdomain-inverted regions formed periodically in the ferroelectricsubstrate, wherein each of the domain-inverted regions has a planarshape with axial symmetry, and the symmetry axes are parallel to eachother, and wherein the domain-inverted regions are formed so that adirection of the symmetry axes is aligned with a Y axis of crystals ofthe ferroelectric substrate, the domain-inverted regions extend from a+Z plane to a −Z plane, and a ratio of an area of the domain-invertedregions penetrating from the upper to the lower surface of theferroelectric substrate with respect to a total area of thedomain-inverted regions is 50% or less, or a mean depth of thedomain-inverted regions is 40% to 95% of a thickness of theferroelectric substrate.
 36. The optical element according to claim 35,wherein the ferroelectric substrate is Mg-doped LiTa_((1−x))Nb_(x)O₃(0≦x≦1).
 37. The optical element according to claim 35, wherein a periodof the domain-inverted regions is 4 μm or less.
 38. The optical elementaccording to claim 35, wherein a thickness of the ferroelectricsubstrate is 1 mm or more.
 39. The optical element according to claim37, wherein a thickness T of the ferroelectric substrate is 1 mm, and aperiod Λ of the domain-inverted regions is 2 μm or less.
 40. The opticalelement according to claim 39, where a depth D of the domain-invertedregions and the thickness T of the ferroelectric substrate satisfy D<T.41. The optical element according to claim 35, wherein an angle θbetween the principal surface and the Z axis is 80°≦θ≦100°.